Table of proposed macroscopic superpositions

Here is a table of proposals for creating enormous superpositions of matter. Importantly, all of them describe superpositions whose spatial extent is comparable to or larger than the size of the object itself. Many are quite speculative. I’d like to keep this table updated, so send me references if you think they should be included.

experimentref.object
composition
object
radius (nm)
nucleon
count
superposition
size (nm)
lifetime
(ms)
repetition
rate (Hz)
KDTLKDTL has been successfully operated, so it is not just a proposal.a  [1-3]OligoporphyrinTo achieve their highest masses, the KDTL interferometer has superposed molecules of functionalized oligoporphyrin, a family of organic molecules composed of C, H, F, N, S, and Zn with molecular weights ranging from ~19,000 Da to ~29,000 Da. (The units here are Daltons, also known as atomic mass units (amu), i.e., the number of protons and neutrons.) The distribution is peaked around 27,000 Da.b  ,00∼1.02.7 × 104100,266100,001.2410,000.00
OTIMA[4-6]Gold (Au),0005.06.0 × 106100,079100,094.0010,600.00
Bateman et al.[7]Silicon (Si),0005.51.1 × 106100,150100,140.0010,000.50
Geraci et al.[8]Silica (SiO2),0006.51.6 × 106100,250100,250.0010,000.50
Wan et al.[9]Diamond (C),0095.07.5 × 109100,100100,000.0510,001.00
MAQRO[10-13]Silica (SiO2),0120.01.0 × 101000,100100,000.0010,000.01
Pino et al.[14]Niobium (Nb)1,000.02.2 × 101300,290100,450.0010,000.10
Stickler et al.The Stickler et al. experiment is a nanorod in an orientation superposition rather than a nanosphere in a position superposition, so I have estimated the effective parameters for the amount of mass superposed in space.c  [15-17]Silicon (Si)1,05.05.0 × 105100,020100,020.0010,05.00
Delić et al.[18]Silica (SiO2)1,071.02.0 × 109100,100100,010.0010,010.00
Marshman et al.[19]Diamond (C)1,100.01.0 × 101020,000101,000.0010,000.10
Wood et al.[20]Diamond (C)1,125.01.7 × 101000,250100,100.0010,001.00

The proposalsKDTL has been implemented.d   above the black line are an updated version of those appearing in Table 1 of my 2017 paper with Itay Yavin. The proposals below the black line have were made more recently. Delić et al. was discussed by me here. Above the line, the repetition rate is either taken directly from the relevant proposal or was estimated based on private correspondence with the authors. Below the line, I have just inverted the the superposition lifetime and added a factor of ten of overhead.

References

[1] S. Gerlich, S. Eibenberger, M. Tomandl, S. Nimmrichter, K. Hornberger, P. J. Fagan, J. Tüxen, M. Mayor, and M. Arndt, Nature communications 2, 263 (2011).
[2] S. Eibenberger, S. Gerlich, M. Arndt, M. Mayor, and J. Tüxen, Physical Chemistry Chemical Physics 15, 14696 (2013).
[3] Y. Fein, P. Geyer, P. Zwick, F. Kiałka, S. Pedalino, M. Mayor, S. Gerlich, and M. Arndt, Nature Physics 15, 1242–1245 (2019).
[4] S. Nimmrichter, P. Haslinger, K. Hornberger, and M. Arndt, New Journal of Physics 13, 075002 (2011).
[5] S. Nimmrichter, K. Hornberger, P. Haslinger, and M. Arndt, Physical Review A 83, 043621 (2011).
[6] M. Arndt and K. Hornberger, Nature Physics 10, 271 (2014).
[7] J. Bateman, S. Nimmrichter, K. Hornberger, and H. Ulbricht, Nature Communications 5, 4788 (2014).
[8] A. Geraci and H. Goldman, Physical Review D 92, 062002 (2015).
[9] C. Wan, M. Scala, G. W. Morley, A. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose, and M. S. Kim, Physical Review Letters 117, 143003 (2016).
[10] R. Kaltenbaek, “Macroscopic quantum experiments in space using massive mechanical resonators (MQES) –
technical note #3,” Tech. Rep., Study conducted under contract with the European Space Agency (2012).
[11] R. Kaltenbaek et al. (MAQRO Collaboration), EPJ Quantum Technology 3, 5 (2016).
[12] R. Kaltenbaek, “Testing quantum physics in space using high-mass matter-wave interferometry,” Proceedings of 50th Rencontres de Moriond; Gravitation: 100 Years after GR, pp. 141 [arXiv:1508.07796] (2015).
[13] R. Kaltenbaek et al., “MAQRO — BPS 2023 Research Campaign Whitepaper” [arXiv:2202.01535] (2022)
[14] H. Pino, J. Prat-Camps, K. Sinha, B. P. Venkatesh, and O. Romero-Isart, Quantum Sci. Technol. 3, 25001 (2018).
[15] B. Stickler, B. Papendell, S. Kuhn, B. Schrinski, J. Millen, M. Arndt, and K. Hornberger, New J. Phys. 20, 122001 (2018).
[16] B. Stickler, K. Hornberger, and M. Kim, Nature Reviews Physics 3, 589–597 (2021).
[17] B. Schrinski, B. Stickler, and K. Hornberger, Phys. Rev. A 105, L021502 (2022).
[18] U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuletić, N. Kiesel, and M. Aspelmeyer, Science 367, 892-895 (2020).
[19] R. Marshman, A. Mazumdar, R. Folman, and S. Bose, “Large Splitting Massive Schrödinger Kittens” [arXiv:2105.01094] (2021).
[20] B. D. Wood, S. Bose, and G. W. Morley, Physical Review A 105, 012824 (2022).

Footnotes

(↵ returns to text)

  1. KDTL has been successfully operated, so it is not just a proposal.
  2. To achieve their highest masses, the KDTL interferometer has superposed molecules of functionalized oligoporphyrin, a family of organic molecules composed of C, H, F, N, S, and Zn with molecular weights ranging from ~19,000 Da to ~29,000 Da. (The units here are Daltons, also known as atomic mass units (amu), i.e., the number of protons and neutrons.) The distribution is peaked around 27,000 Da.
  3. The Stickler et al. experiment is a nanorod in an orientation superposition rather than a nanosphere in a position superposition, so I have estimated the effective parameters for the amount of mass superposed in space.
  4. KDTL has been implemented.
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